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and then distributed them as George had desired. How many twentieths did he give to each?

33. # is how many zo? } is how many zo? is how many z ? Ty is how many zt?

34. 4 is how many to? 35. 4 is how many ? 36. 1 is how many ? 37. 'is how many 15?

are how many ? 39. are how many 4?.

is how many to? are how many tis? & are how many it?

are how many 1? 44. & are how many ? 45. are how many ?

are how many t?. 47. 3 are how many ? 48. Reduce I to sixths and * to sixths. . 49. X and 2 are how many ? 50. Reduce and 1 to eighths. 51. 1 and 1 are how many ? 52. I and I are how many ? 53. & and I are how many ? 54. Å and are how many }? 55. and are how many ? 56. and are how many th?

and 1 and f are how many f?,

and 3 and I are how many ? 59. and 1 are how many ? 60. and 1 and 1 are how many I'?

and y, and I are how many ato?

and 1 and and I and I are how many It? 63. 1 and are how many it?

and j are how many t's? 65. and are how many 15? 66. g less are how many t.?

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67. and , less B, are how many t?

68. less are how many ? - 69. less g are how many z4?.

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73. and are how many ?
74. and are how many so?
75. and 4 are how many ?

When the denominators in two or more fractions are the same, the fractions are said to have a common denominator. Thus and of have a common denominator. We have seen that, when two or more fractions have a common denominator, they may be added and subtracted as well as whole numbers. We add or subtract the numerators, and write their sum or difference over the common denominator. The first part of the process in the above examples was to reduce them to a common denominator.

76. Reduce and to a common denominator, NOTE. They may be reduced to twelfths.

If it cannot be immediately seen what number must be the common denominator, it may be found by multiplying all the denominators together ; for that will always produce a number divisible by all the denominators.

77. Reduce and to a common denominator.

78. Reduce and fand & to a common denominator.

79. Reduce and to a common denominator. 30. Reduce and * to a common denominatok

81. Reduce and and to a common denominator.

82. Add together and .
83. Add together 3 and
84. Add together and is
85. Add together and f and to
86. Subtract from f.
87. Subtract from
88. Subtract & from ...
89. Subtract from

B. 1. Mr. F. said he would give 4 of a pine-apple to Fanny, and to George, and the rest to the one that could tell how to divide it, and how much there would be left. But neither of them could tell; so he kept it himself. Could you have told if you had been there? How would you divide it? How much would be left ?

2. A man sold it bushels of wheat to one man, 4 bushels to another; how many bushels did he sell to both ?

3. A man bought 64 bushels of wheat at one time, and 2 at another; how much did he buy in the whole ?

4. A man bought 7 yards of one kind of cloth, and 6yards of another kind; how many yards in the whole ?

5. A man bought of a barrel of beer at one time, 21 barrels at another, and 6 at another; how much did he buy in the whole ?

6. A man bought one sheep for 4 dollars, and apother for 54 dollars ; how much did he give for both ?

7. There is a pole standing, so that of it is in the mud, and of it in the water, and the rest out of the water ; how much of it is out of the water?

8. A man, having undertaken to do a piece of work, did of it the first day, of it the second day, and of it the third day; how much of it did he do in three days ?

9. A man, having a piece of work to do, hired two men and a boy to do it. The first man could do of the work in a day, and the other of it, and the boy of it; how much of it would they all do in a day?

C. It will be seen, by looking on plate III. that? is the same as , and that is the same as y, and that is the same as ; 2, 8, can therefore be reduced to , and 4 to. This is called reducing fractions to their lowest terms.

1. Reduce to its lowest terms. * Ans. *. 2. Reduce 5 to its lowest terms. 3. Reduce to its lowest terms. 4. Reduce to its lowest terms. 5. Reduce 14 to its lowest terms. 6. Reduce to its lowest terms. 7. Reduce to its lowest terms. 8. Reduce 18 to its lowest terms. 9. Reduce to its lowest terms. 10. Reduce to its lowest terms. 11. Reduce as to its lowest terms. 12. Reduce ļ to its lowest terms. 13. Reduce 43 to its lowest terms. 14. Reduce to its lowest terms.

Note. It will be seen by the above section, that, if both the numerator and denominator be multiplied by the same number, the value of the fraction will not be altered; or, if they can both be divided by the same number without a remainder, the fraction will not be altered.

* If this article should be found ton difficult for the pupil, he may omit it till after the next section.

SECTION XIV.

A. 1. A Boy, having of an orange, gave away ? of that; what part of the whole orange did he give away?

2. What is 4 of 1?

3. If you cut an apple into three pieces, and then cut each of those pieces into two pieces, how many pieces will the whole apple be cut into ? What part of the whole apple will one of the pieces be?

4. What is 1 of 1?

5. A boy had l of a pine-apple, and cut that half into three pieces, in order to give away of it. What part of the whole apple did he give away?

6. What is f of 1 ?

17. If an orange be cut into 4 parts, and then each of the parts be cut in two, how many pieces will the whole be cut into ?

8. What is 4 of ?

9. A man, having } a barrel of four, sold # of that ; how much did he sell ?

10. What is of ?

11. If an orange be cut into 4 equal parts, and each of those parts be cut into 3 equal parts, how many parts will the whole orange be cut into ?"

12. What is of ?

13. A boy, having } of a quart of chestnuts, gave away 1 of what he had. What part of the whole quart did he give away ?

14. What is t of {?
15. What is I of 1?

16. A man, owning * of a ship, sold of his share; what part of the ship did he sell, and what part did he then own?

17. What is ļof ?
18. What is of 1?

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